Set of nine graphs illustrating various mathematical functions and relations, including linear, piecewise, and circular forms, with attention to domain and range restrictions.

It looks like you've uploaded a set of graphs labeled A through L, and the instruction says: "USE THESE GRAPHS TO ANSWER QUESTIONS 1 – 12." However, I don’t see any specific questions listed in your message. The image contains 12 graphs (A–L), but without the actual questions (e.g., identifying functions, domain/range, continuity, symmetry, etc.), I can't directly solve or answer them.

But I can help you analyze each graph and explain their key features so that you can use this information to answer typical questions that might be associated with such a set (like identifying which are functions, determining domains and ranges, checking for symmetry, etc.).

Let me go through each graph briefly and describe its properties:

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Graph A

- A piecewise linear graph.
- Starts at (-4, 3), goes down to (-2, 1), up to (0, 5), down to (2, 1), then up to (4, 3).
- All points are filled (closed circles), so endpoints are included.
- Domain: [-4, 4]
- Range: [1, 5]
- Is it a function? Yes — passes vertical line test.
- Symmetry? Not symmetric.

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Graph B

- A straight line segment from (-6, -2) to (4, 2), but open circle at (4, 2) → not included.
- So, endpoint at x = 4 is excluded.
- Domain: [-6, 4)
- Range: [-2, 2)
- Function? Yes — straight line, passes vertical line test.
- Continuous? No — open endpoint at right.

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Graph C

- Vertical line segment from (-2, 3) to (-2, -3), both ends are open circles → not included.
- So, it’s just the line x = -2, y ∈ (-3, 3)
- Domain: {-2}, but since endpoints are open, technically no point is included → empty set?
- Wait: if both ends are open, and it's a continuous segment between them, it's x = -2, y ∈ (-3, 3), but not including y = ±3.
- But vertical line → not a function (fails vertical line test).
- Domain: {-2}
- Range: (-3, 3)
- Function? No

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Graph D

- A circle centered at origin, radius ~4 units.
- Equation: $ x^2 + y^2 = 16 $
- Domain: [-4, 4]
- Range: [-4, 4]
- Function? No — fails vertical line test (many y-values for one x).
- Symmetric? Symmetric about both axes and origin.

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Graph E

- Two curves forming a "U" shape opening to the right.
- Looks like a sideways parabola: $ x = y^2 $
- Starts at (0, 0) and extends to the right.
- Points at end have arrows → infinite extension.
- Domain: [0, ∞)
- Range: (-∞, ∞)
- Function? No — fails vertical line test (one x has two y-values).
- Symmetric? About x-axis.

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Graph F

- Horizontal ray starting at (-2, 0) with open circle, going to the right (→).
- So: x > -2, y = 0
- Domain: (-2, ∞)
- Range: {0}
- Function? Yes — constant function on interval.
- Continuous? No — open at left.

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Graph G

- Horizontal line segment from (-2, -1) to (2, -1), with open circle at (-2, -1), closed at (2, -1).
- So: x ∈ (-2, 2], y = -1
- Domain: (-2, 2]
- Range: {-1}
- Function? Yes
- Continuous? No — open on left.

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Graph H

- Diagonal line segment from (-2, 2) to (2, -2), both endpoints closed.
- Slope = -1, passes through origin.
- Domain: [-2, 2]
- Range: [-2, 2]
- Function? Yes
- Symmetric? About origin (odd function)

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Graph I

- V-shaped graph, vertex at (0, 0), opens upward.
- Lines go to (-2, 2) and (2, 2), both ends are open circles.
- So: y = |x|, but only defined for x ∈ (-2, 2), excluding endpoints.
- Domain: (-2, 2)
- Range: [0, 2)
- Function? Yes
- Symmetric? About y-axis (even function)

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Graph J

- Not visible in your image — possibly cut off.

Wait, let's count:
You have A–I shown, and then J, K, L are below but not fully visible.

But based on what's visible, we have:

- A–I: fully visible
- J, K, L: likely partially or not shown.

Assuming the rest are missing, I’ll proceed assuming the questions are standard ones like:

> Which graphs represent functions?
> Which are continuous?
> Which are symmetric?
> What are the domain and range?

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Common Types of Questions (and Answers):

#### Q1: Which graphs represent functions?
Use vertical line test.

- Functions: A, B, F, G, H, I
- Not functions: C, D, E

> ✔ A, B, F, G, H, I → YES
> ✘ C, D, E → NO

(We need to check J, K, L, but they're not visible.)

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#### Q2: Which graphs are continuous?
- Continuous if no breaks, jumps, or holes.

- A: Continuous ✔
- B: Open at right → discontinuous ✘
- C: Open at both ends → discontinuous ✘
- D: Circle → continuous ✔
- E: Two branches → continuous on each branch, but not a function; overall continuous? Yes, as a curve, but not a function.
- F: Open at left → discontinuous ✘
- G: Open at left → discontinuous ✘
- H: Closed endpoints → continuous ✔
- I: Open at ends → discontinuous ✘

So continuous graphs: A, D, E, H
(Note: E is continuous as a curve, even though not a function.)

But if question asks for functions that are continuous, then: A, H

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#### Q3: Which graphs have symmetry?

- Even (symmetric about y-axis): I (V-shape), maybe A? Let's check:
- A: Not symmetric — left and right not mirror images.
- I: Yes ✔
- D: Circle → symmetric about both axes and origin ✔
- H: Odd function (symmetric about origin) ✔
- B: Not symmetric
- F: Not symmetric
- G: Not symmetric
- E: Symmetric about x-axis ✔
- C: Symmetric about x-axis? Yes — vertical line, symmetric top/bottom

So:
- Symmetric about y-axis: I, D
- Symmetric about x-axis: E, C
- Symmetric about origin: H, D

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Summary Table

| Graph | Function? | Continuous? | Domain | Range | Symmetry |
|-------|-----------|-------------|--------|-------|----------|
| A | Yes | Yes | [-4,4] | [1,5] | None |
| B | Yes | No | [-6,4) | [-2,2)| None |
| C | No | No | {-2} | (-3,3)| x-axis |
| D | No | Yes | [-4,4] | [-4,4]| All |
| E | No | Yes | [0,∞) | ℝ | x-axis |
| F | Yes | No | (-2,∞) | {0} | None |
| G | Yes | No | (-2,2] | {-1} | None |
| H | Yes | Yes | [-2,2] | [-2,2]| Origin |
| I | Yes | No | (-2,2) | [0,2) | y-axis |

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Final Notes:

Since the questions 1–12 are missing, I cannot give exact answers. But here are common questions and how to answer them using the above analysis:

- Which are functions? → A, B, F, G, H, I
- Which are continuous? → A, D, E, H
- Which have domain all real numbers? → Only D and E (but D is not a function)
- Which have restricted domain? → All except D and E (if considering full extent)
- Which are odd functions? → H
- Which are even functions? → I
- Which are constant functions? → F, G
- Which represent a circle? → D
- Which is a vertical line? → C
- Which is a horizontal line? → F, G
- Which is a parabola? → E (sideways)

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👉 Please provide the actual questions (1–12) so I can give precise answers.

Or, if you want, I can generate sample questions and answers based on these graphs.